An online cross product calculator determines the cross-product for three dimensions. Our innovative vector multiplication calculator aims to simplify and streamline magnitude, direction, and normalize vectors, and spherical coordinates.
The cross product is the vector quantity that indicates both direction and magnitude and it also measures how much two vectors point in different directions.
Our vector calculator computes the cross-product between the types of vectors.
The cross product calculator is a way to calculate the product of two vectors. The formula used for the calculation is as follows:
C = a x b = |a| x |b| x sinθ x n
Where:
You can try our Trapezoid area calculator to find the area and parameters of trapezoid shapes.
Our right hand rule calculator is used to find the direction and magnitude of cross product vectors. It aid’s in determining the resultant vector’s direction.
The statement of the right-hand rule is as follows:
If you point your figure in the direction of the moving positive charges and your middle finger points in the direction of the magnetic field and your thumb indicates the magnetic force that pushes the moving charges.
The procedure to calculate the magnitude and direction by our cross product calculator is as follows. Let's take a look at the example below.
Let’s consider two vectors
$$ \vec u = 2\vec i – \vec j + 3\vec k $$
$$ \vec v = 5\vec i + 7\vec j – 4\vec k $$
Set up the cross product matrix
$$ \vec u \times \vec v = \begin{vmatrix} i& j& k&\\ 2& -1& 3& \\ 5& 7& -4& \end{vmatrix} $$
Finally, calculate the determinants of the metrics
$$ \vec u \times \vec v = (4 – 21)\vec i – (-8 – 15)\vec j + (14 + 5)\vec k $$
$$ \vec u \times \vec v = -17\vec i + 23\vec j + 19\vec k $$
If two vectors have the same direction or have opposite directions from each other means that they are not linearly independent. Then their cross-product is equal to zero. More generally the magnitude of the product of two perpendicular vectors is the product of their lengths.
You can also use our standard form calculator to compute the numerical expressions into their standard form.
The vector product calculator is loaded with a user-friendly interface that shows the cross-product of the vectors within a couple of seconds. Just stick to the given steps to find the cross product by the cross product vector calculator.
Input:
Output:
Our vector cross product calculator determines the following results:
The cross-product can be used in determining the followings:
The cross product indicates the direction and magnitude so it is a vector.
The cross product of two vectors is always perpendicular. It is defined as the vector c that is perpendicular to the vectors a and b with directions and magnitude equal to the area of the parallelogram.
It has a wide range of applications in different fields
From the source Wikipedia: Cross product, Definition, Computing, Properties, Alternative ways to compute, Applications, As an external product, Generalizations.
From the source Khan Academy: Cross products, properties of the cross product, The right-hand rule, matrices intro, determinants.
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